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 Just a fraction off (Posted on 2006-05-28)

Egyptian Fractions are fractions expressed in the form of 1/n or as the sum of such fractions (1/a + 1/b + ...). For example, 2/3 would be expressed as 1/2 + 1/6.
(As found on the Rhind papyrus, 2/3 was one, if not the only, non-unit fraction used by the Egyptians.)

The following Egyptian Fractions correspond to the fractional portion of the first ten non-integer members of a "regular" series. (The "whole number" component of each member of the series is omitted and any series members without fractional components is likewise omitted).

What is the missing fraction in this sequence?

1/2 + 1/14
1/4 + 1/44
1/4 + 1/18 + 1/468
1/4 + 1/28
1/2
1/2 + 1/4 + 1/14 + 1/476
1/19
1/2 + 1/3 + 1/42
1/2 + 1/8 + 1/88
1/3 + ?

 See The Solution Submitted by Dej Mar Rating: 3.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: The busy work | Comment 2 of 7 |
(In reply to The busy work by Jyqm)

Jyqm, before this became public, I did the same arithmetic as you.

I queried the author about the 'integers'.

The following Egyptian Fractions correspond to the fractional portion of the first ten non-integer members of a "regular" series. (The "whole number" component of each member of the series is omitted and any series members without fractional components is likewise omitted).

and remembering the reply, this series is stripped of the integers.  We need to supply them to solve the 'regular' sequence, whatever it may be.

(I wasn't concerned about the 1/2 but the 33/128 bugged me!  Did we let a typo slip through? Should 128 have been 129 so that
33/128 is really 33/129 and thus 11/43?)

Dej Mar? Is the problem as posted correct, please?

 Posted by brianjn on 2006-05-29 08:20:45

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